Modulated rotating waves in the magnetized spherical Couette system

Abstract

We present a study devoted to a detailed description of modulated rotating waves (MRW) in the magnetized spherical Couette system. The set-up consists of a liquid metal confined between two differentially rotating spheres and subjected to an axially applied magnetic field. When the magnetic field strength is varied, several branches of MRW are obtained by means of three dimensional direct numerical simulations (DNS). The MRW originate from parent branches of rotating waves (RW) and are classified according to Rand's (Arch. Ration. Mech. Anal 79:1-37, 182) and Coughling & Marcus (J. Fluid Mech. 234:1-18,1992) theoretical description. We have found relatively large intervals of multistability of MRW at low magnetic field, corresponding to the radial jet instability known from previous studies. However, at larger magnetic field, corresponding to the return flow regime, the stability intervals of MRW are very narrow and thus they are unlikely to be found without detailed knowledge of their bifurcation point. A careful analysis of the spatio-temporal symmetries of the most energetic modes involved in the different classes of MRW will allow in the future a comparison with the HEDGEHOG experiment, a magnetized spherical Couette device hosted at the Helmholtz-Zentrum Dresden-Rossendorf.

Contains 3 tables and 8 figures. Published in the Journal of Nonlinear Science

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• Long term time dependent frequency analysis of chaotic waves in the weakly magnetized spherical Couette system
• High dimensional tori and chaotic and intermittent transients in magnetohydrodynamic Couette flows
• On the annual and semi-annual components of variations in extent of Arctic and Antarctic sea-ice
• Modulated rotating waves and triadic resonances in spherical fluid systems: The case of magnetized spherical Couette flow